Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Miguel received a \(100 gift certificate for a graduation gift. He wants to buy a CD player that costs \)38 and CDs that cost $12 each. Which of the following inequalities represents how many CDs Miguel can buy?

A$\mathit{n}\mathbf{\le }\mathbf{6}$

B$\mathit{n}\mathbf{\le }\mathbf{6}$

C$\mathit{n}\mathbf{<}\mathbf{5}$

D$\mathit{n}\mathbf{\le }\mathbf{5}$

Short answer

The inequality that represents the number of CDs that Miguel can buy is $\mathit{n}\mathbf{\le }\mathbf{5}$. Therefore, the option Dis correct.

Step-by-step solution

Step 1. Write the inequality for the given problem.

It is given that Miguel has $100 and the cost of a CD player is $38 and the cost of 1 CD is $12.

Let $n$be the number of CDs that Miguel can buy.

As, the cost of 1 CD is $12, therefore the cost of CDs is $\$\left(12n\right)$.

The cost of 1 CD player and $n$CDs is $\$\left(12n+38\right)$.

As, Miguel has $100. Therefore, the maximum amount that Miguel can spend is $100.

Therefore, the cost of 1 CD player and CDs should be less than or equal to $100.

Therefore, the inequality for the given problem is:

$12n+38\le 100$

Step 2. Find the inequality that represents the number of CDs that Miguel can buy.

The inequality for the given problem is:

$12n+38\le 100$

Solve the inequality $12n+38\le 100$.

$\begin{array}{c}12n+38\le 100\\ 12n+38-38\le 100-38\\ 12n\le 62\\ n\le \frac{62}{12}\\ n\le 5.1667\\ n\le 5\end{array}$

Therefore, the inequality that represents the number of CDs that Miguel can buy is $n\le 5$. Therefore, the option Dis correct.